Final answer:
The concentration of silver ions, [Ag+], in a solution initially 0.113 M with respect to Ag(NH3)2+ and given a Kf of 1.7 x 10^7, is assumed to go to completion, resulting in a silver ion concentration of 0.113 M.
Step-by-step explanation:
Calculating Silver Ion Concentration
To calculate the concentration of silver ions, [Ag+], in a solution with an initial concentration of 0.113 M with respect to Ag(NH3)2+, and given the formation constant (Kf) of 1.7 x 107, we will assume that the reaction goes to completion due to the very high Kf value. The dissociation of the complex ion can be represented as:
Ag(NH3)2+ (aq) ⇌ Ag+ (aq) + 2NH3 (aq)
Since the formation of the complex ion is favored, virtually all of the Ag(NH3)2+ will dissociate into Ag+ and NH3. This implies that the initial concentration of the complex ion, which is 0.113 M, will approximately be the same as the concentration of silver ions in the solution, hence [Ag+] = 0.113 M.
This method of calculation is applicable due to the equilibrium strongly favoring the formation of the complex ion, which is indicated by the large value of Kf. Such cases often occur in coordination chemistry, where a transition metal ion forms a stable complex with ligands, in this case, ammonia.